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Question Number 227139    Answers: 2   Comments: 0

Question Number 226919    Answers: 4   Comments: 0

Question Number 226798    Answers: 1   Comments: 0

let gcd(m,n)=1. Determine gcd(5^m +7^m ,5^n +7^n )

$${let}\:{gcd}\left({m},{n}\right)=\mathrm{1}.\:{Determine}\:{gcd}\left(\mathrm{5}^{{m}} +\mathrm{7}^{{m}} ,\mathrm{5}^{{n}} +\mathrm{7}^{{n}} \right) \\ $$

Question Number 226779    Answers: 1   Comments: 0

By using De Moivres theorm simplify (a)(((cos (π/2)−isin (π/2))(cos (π/3)+isin (π/3)))/(cos (π/3)−isin (π/3))) (b)((cos (π/8)+isin (π/8))/(cos (π/6)+isin (π/6)))

$${By}\:{using}\:{De}\:{Moivres}\:{theorm} \\ $$$${simplify} \\ $$$$\left({a}\right)\frac{\left(\mathrm{cos}\:\frac{\pi}{\mathrm{2}}−{i}\mathrm{sin}\:\frac{\pi}{\mathrm{2}}\right)\left(\mathrm{cos}\:\frac{\pi}{\mathrm{3}}+{i}\mathrm{sin}\:\frac{\pi}{\mathrm{3}}\right)}{\mathrm{cos}\:\frac{\pi}{\mathrm{3}}−{i}\mathrm{sin}\:\frac{\pi}{\mathrm{3}}} \\ $$$$\left({b}\right)\frac{\mathrm{cos}\:\frac{\pi}{\mathrm{8}}+{i}\mathrm{sin}\:\frac{\pi}{\mathrm{8}}}{\mathrm{cos}\:\frac{\pi}{\mathrm{6}}+{i}\mathrm{sin}\:\frac{\pi}{\mathrm{6}}} \\ $$

Question Number 226775    Answers: 0   Comments: 0

Prove that (a−b)(a−c)(a−d)(b−c)(b−d)(c−d) divisible by 12

$${Prove}\:{that}\:\left({a}−{b}\right)\left({a}−{c}\right)\left({a}−{d}\right)\left({b}−{c}\right)\left({b}−{d}\right)\left({c}−{d}\right)\:{divisible}\:{by}\:\mathrm{12} \\ $$

Question Number 226721    Answers: 4   Comments: 0

Question Number 226697    Answers: 1   Comments: 1

Question Number 226612    Answers: 0   Comments: 1

Question Number 226608    Answers: 1   Comments: 0

Question Number 226609    Answers: 3   Comments: 0

Question Number 226586    Answers: 0   Comments: 0

Question Number 226585    Answers: 0   Comments: 0

Question Number 226513    Answers: 2   Comments: 0

Find gcd(a^2 +ab+b^2 ,ab) if gcd(a,b)=1

$${Find}\:{gcd}\left({a}^{\mathrm{2}} +{ab}+{b}^{\mathrm{2}} ,{ab}\right)\:{if}\:{gcd}\left({a},{b}\right)=\mathrm{1} \\ $$

Question Number 226464    Answers: 0   Comments: 2

Question Number 226455    Answers: 1   Comments: 0

Question Number 226177    Answers: 0   Comments: 0

Question Number 226943    Answers: 4   Comments: 3

Question Number 226942    Answers: 4   Comments: 0

Question Number 226006    Answers: 0   Comments: 2

(3/7)^0 prove and evalute show all working

$$\left(\mathrm{3}/\mathrm{7}\right)^{\mathrm{0}} \:\:\:{prove}\:{and}\:{evalute}\:{show}\:{all} \\ $$$${working} \\ $$

Question Number 225599    Answers: 1   Comments: 2

Question Number 224691    Answers: 1   Comments: 0

3k+4=n^2 . k,n ∈N Find all n numbers .

$$\mathrm{3}{k}+\mathrm{4}={n}^{\mathrm{2}} .\:{k},{n}\:\in\mathbb{N} \\ $$$${Find}\:{all}\:{n}\:{numbers}\:. \\ $$

Question Number 224443    Answers: 1   Comments: 0

Same problem with me please fix the problem

$$ \\ $$$$\boldsymbol{{S}}{ame}\:{problem}\:{with}\:{me} \\ $$$${please}\:{fix}\:{the}\:{problem} \\ $$

Question Number 224305    Answers: 1   Comments: 0

Question Number 224100    Answers: 1   Comments: 0

Calculate I=∫^( +∞) _( 0) [(1/t)−(1/(sh(t)))]^( 2) dt

$$\mathrm{Calculate}\:\mathrm{I}=\underset{\:\mathrm{0}} {\int}^{\:+\infty} \left[\frac{\mathrm{1}}{\mathrm{t}}−\frac{\mathrm{1}}{\mathrm{sh}\left(\mathrm{t}\right)}\right]^{\:\mathrm{2}} \mathrm{dt} \\ $$

Question Number 223570    Answers: 0   Comments: 0

demontrer que quelque soit k appartenant N l

$${demontrer}\:{que}\:{quelque}\:{soit}\:{k}\:{appartenant}\:{N}\:\:{l} \\ $$

Question Number 223414    Answers: 1   Comments: 0

is it possible to prove that mn(m+n)(m−n) divisible by 6 always

$${is}\:{it}\:{possible}\:{to}\:{prove}\:{that}\:{mn}\left({m}+{n}\right)\left({m}−{n}\right)\: \\ $$$${divisible}\:{by}\:\mathrm{6}\:{always}\:\:\:\:\:\:\:\:\:\: \\ $$

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